Consider the specific heats h2o(s) = 2.09 j/g · ◦c, h2o (ℓ) = 4.18 j/g · ◦c, and h2o(g) = 2.03 j/g · ◦c. the heat of fusion for water is 334 j/g and its heat of vaporization is 2260 j/g. calculate the amount of heat required to convert 59 g of ice at −35◦c completely to liquid water at 55◦c. answer in units of kj.

Refer to the diagrams shown below.

Goal:
We want to determine the amount of heat required to convert 59 g of ice at  -35 °C to liquid water at 55 °C.

Given:
c = 2.09 J/(g-°C), the specific heat of ice
   = 4.18  J/(g-°C), the specific heat of water
   = 2.03 J/(g-°C), the specific heat of steam

L = 334 J/g, the latent heat of fusion of water
   = 2260 J/g, the latent heat of vaporization of water 

Stage 1: Convert ice at  -35 °C to ice at 0 °C.
The heat required is
Q₁ = (59 g)*(2.09 J/(g-°C))*(0-(-35) °C) = 4,315.85 J

Stage 2: Convert ice at 0 °C to water at 0 °C.
The heat required is
Q₂ = (59 g)*(334 J/g) = 19,706 J

Stage 3: Raise the temperature of the water from 0 °C to 55 °C.
The heat required is
Q₃ = (59 g)*(4.18 J/(g-°C))*(55 °C) = 13,564.10 J

The total heat required is
Q = Q₁ + Q₂ + Q₃ = 37,585.95 J = 37.586 kJ

37.6 kJ

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